login
a(n) = A349434(n) + A349435(n).
3

%I #10 Nov 21 2021 01:19:08

%S 2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,8,0,0,

%T 0,12,0,0,0,0,0,0,0,0,0,0,0,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,20,0,0,0,

%U 0,0,0,0,0,0,0,0,0,0,0,0,-8,9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-8,0,0,0,20,0,0,0,0,0,0,0,12

%N a(n) = A349434(n) + A349435(n).

%H Antti Karttunen, <a href="/A349436/b349436.txt">Table of n, a(n) for n = 1..20000</a>

%F a(1) = 2, and for n >1, a(n) = -Sum_{d|n, 1<d<n} A349434(d) * A349435(n/d). [As the sequences are Dirichlet inverses of each other]

%t s[n_] := n * DivisorSum[n, 1/# &, !CompositeQ[#] &]; sinv[1] = 1; sinv[n_] := sinv[n] = -DivisorSum[n, sinv[#] * s[n/#] &, # < n &]; f[p_, e_] := e/p; d[1] = 1; d[n_] := n*(1 + Plus @@ f @@@ FactorInteger[n]); dinv[1] = 1; dinv[n_] := dinv[n] = -DivisorSum[n, dinv[#] * d[n/#] &, # < n &]; a[n_] := DivisorSum[n, dinv[#] * s[n/#] + sinv[#] * d[n/#] &]; Array[a, 100] (* _Amiram Eldar_, Nov 18 2021 *)

%o (PARI) A349436(n) = (A349434(n) + A349435(n)); \\ Needs also code from A349434 and A349435.

%Y Cf. A349434, A349435.

%K sign

%O 1,1

%A _Antti Karttunen_, Nov 17 2021